What is inverse oflaplace (s-2)/(s^2-7s+6) ?

The answer to inverse oflaplace (s-2)/(s^2-7s+6) is 1/5 e^t+4/5 e^{6t}

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inverse oflaplace (s-2)/(s^2-7s+6)

inverse laplace

\frac{s - 2}{s ^{2} - 7 s + 6}

\frac{1}{5} e^{t} + \frac{4}{5} e^{6 t}

Solution steps

L^{- 1} {\frac{s - 2}{s ^{2} - 7 s + 6}}

Take the partial fraction of

\frac{s - 2}{s ^{2} - 7 s + 6} : \frac{1}{5 ( s - 1 )} + \frac{4}{5 ( s - 6 )}

= L^{- 1} {\frac{1}{5 ( s - 1 )} + \frac{4}{5 ( s - 6 )}}

Use the linearity property of Inverse Laplace Transform:

For functions

f (s), g (s)

and constants

a, b : L^{- 1} {a \cdot f (s) + b \cdot g (s)} = a \cdot L^{- 1} {f (s)} + b \cdot L^{- 1} {g (s)}

= L^{- 1} {\frac{1}{5 ( s - 1 )}} + L^{- 1} {\frac{4}{5 ( s - 6 )}}

L^{- 1} {\frac{1}{5 ( s - 1 )}} : \frac{1}{5} e^{t}

L^{- 1} {\frac{4}{5 ( s - 6 )}} : \frac{4}{5} e^{6 t}

= \frac{1}{5} e^{t} + \frac{4}{5} e^{6 t}

x^{- 6} + e^{2 x}

\frac{d y}{d x} + 2 x y = x

\int \frac{1}{24} x^{2} d x

\frac{\partial}{\partial x} (- x + 6 y)

\frac{d}{d x} (ln (5 + ln (x)))

What is inverse oflaplace (s-2)/(s^2-7s+6) ?
The answer to inverse oflaplace (s-2)/(s^2-7s+6) is 1/5 e^t+4/5 e^{6t}